Role of Arterial Stenosis on Non-Newtonian Flow of Blood in Presence of Slip Velocity

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American Journal of Engineering Research (AJER) 2016 American Journal of Engineering Research (AJER) e-ISSN: 2320-0847 p-ISSN : 2320-0936 Volume-5, Issue-12, pp-326-333 www.ajer.org Research Paper Open Access

Role of Arterial Stenosis on Non-Newtonian Flow of Blood in Presence of Slip Velocity Arun Kumar Maiti (Department of Mathematics, Shyampur Siddheswari Mahavidyalaya, India)

ABSTRACT: An attempt has been made to study the role of arterial stenosis on blood flow in presence of slip velocity. In the present analysis Herschel-Bulkley fluid represents the non-Newtonian character of blood. The hemodynamic behaviour of blood flow is influenced by the presence of arterial stenosis. The expressions for velocity profile, pressure drop and shear stress have been investigated here. The results are shown in graphical form. Keywords: Herschel-Bulkley fluid, Shear Stress, Yield Stress, Stenosis, Resistance to flow.

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INTRODUCTION

Many cardiovascular diseases, such as stroke, atherosclerosis, which are responsible for major cause of death, are closely related to the nature of blood flow and the dynamic behaviour of blood vessels. It is well known from medical point of view that many cardiovascular diseases directly depend on various types of arterial diseases. Among the arterial diseases the most important one is stenosis. The medical term stenosis means narrowing of body passage, including blood vessels, heart valves, vertebral canal, G. I. tract. It is believed that stenosis is formed by the accumulation of fatty substances like cholesterol or fats in the inner wall of the artery and proliferation of connecting cells. If stenosis is present in an artery, the blood flow changes to its usual state, because resistance to flow is increased and as a result supply of oxygen to each cell of the body and removal of carbon dioxide is disturbed abruptly. In other words nutrient supplement is insufficient to reach each cell of the body. Many bio-medical researchers (Shukla et. al. [1], Young and Tsai [2], Verma and Parihar [3]) feel that the hemodynamic factors may be helpful in the diagnosis, treatment and understanding of many disorders. Misra and Shit [4] have developed a mathematical model to study the non-Newtonian aspect of blood flow by using Herschel-bulkley fluid model in presence of arterial stenosis and they have shown that skin friction and resistance to flow is maximum at the throat of the stenosis and minimum at the end. Ali et. al. [5] have analysed the effect of an axial symmetric time dependent growth along the lumen of the arterial tube by considering blood as a Newtonian fluid. Biswas and Chakraborty [6], srivastava et. al. [7] have studied nonNewtonian behaviour of blood through a stenosed artery. Shah and Siddiqui [8] have studied a mathematical model to analyze the effect of peripheral layer viscosity on blood flow through stenosed arterial tube by considering the blood as power-law type non-Newtonian fluid. They have seen that the peripheral layer viscosity of blood in diabetic patients is higher than in non-diabetic patients, resulting higher resistance to flow.So peripheral layer viscosity has significant effects on resistance to flow. Thus resistance to blood flow of diabetic patients may be reduced by reducing the plasma layer viscosity. Many researchers (Vershney et. al. [9], Singh and Shah [10], Sankar and Hemalatha [11], Sankar [12], Sanyal and Maiti [13]) have presented various types of mathematical models to study various characteristics of blood by considering blood as a non- Newtonian fluid. Many investigators (Nuber [14], Haymen [15], Chaturani and Biswas [16], Kumar et. al. [17], Biswas and Chakraborty [18], Chaturani and Ponalagusamy [19]) have analysed theoretically the blood flow model through uniform artery in presence of slip velocity to study the flow parameters of blood. In a recent paper Biswas and Laskar [20] have presented a mathematical model to study the effect of slip velocity on steady flow of blood through constricted artery.

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